1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26 * SUCH DAMAGE.
27 */
28
29 #include <float.h>
30
31
32 #define BIAS (LDBL_MAX_EXP - 1)
33 #define MANH_SIZE (EXT_FRACHBITS + 1)
34
35 /* Approximation thresholds. */
36 #define ASIN_LINEAR (BIAS - 56) /* 2**-56 */
37 #define ACOS_CONST (BIAS - 113) /* 2**-113 */
38 #define ATAN_CONST (BIAS + 113) /* 2**113 */
39 #define ATAN_LINEAR (BIAS - 56) /* 2**-56 */
40
41 /* 0.95 */
42 #define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
43
44 /* Constants shared by the long double inverse trig functions. */
45 #define pS0 _ItL_pS0
46 #define pS1 _ItL_pS1
47 #define pS2 _ItL_pS2
48 #define pS3 _ItL_pS3
49 #define pS4 _ItL_pS4
50 #define pS5 _ItL_pS5
51 #define pS6 _ItL_pS6
52 #define pS7 _ItL_pS7
53 #define pS8 _ItL_pS8
54 #define pS9 _ItL_pS9
55 #define qS1 _ItL_qS1
56 #define qS2 _ItL_qS2
57 #define qS3 _ItL_qS3
58 #define qS4 _ItL_qS4
59 #define qS5 _ItL_qS5
60 #define qS6 _ItL_qS6
61 #define qS7 _ItL_qS7
62 #define qS8 _ItL_qS8
63 #define qS9 _ItL_qS9
64 #define atanhi _ItL_atanhi
65 #define atanlo _ItL_atanlo
66 #define aT _ItL_aT
67 #define pi_lo _ItL_pi_lo
68
69 #define pio2_hi atanhi[3]
70 #define pio2_lo atanlo[3]
71 #define pio4_hi atanhi[1]
72
73 /* Constants shared by the long double inverse trig functions. */
74 extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
75 extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
76 extern const long double atanhi[], atanlo[], aT[];
77 extern const long double pi_lo;
78
79 static inline long double
P(long double x)80 P(long double x)
81 {
82
83 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
84 (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
85 pS9))))))))));
86 }
87
88 static inline long double
Q(long double x)89 Q(long double x)
90 {
91
92 return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \
93 (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
94 }
95
96 static inline long double
T_even(long double x)97 T_even(long double x)
98 {
99
100 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
101 (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
102 (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
103 }
104
105 static inline long double
T_odd(long double x)106 T_odd(long double x)
107 {
108
109 return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
110 (aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \
111 (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
112 }
113